Question

if tan(πcosx)=cot(πsinx) then prove that cos(x-π/4)=+-1/2√2

Answer 1

tan ( π cos x ) = cot ( π sin x ) 

tan ( π cos x ) = tan [ ±π/2 - π sin x ]  
As we know that  cot θ = tan ( ±π/2- θ ) 

π cos x = ±π/2 - π sin x 

cos x = ±1/2 - sin x 

cos x + sin x = ±1/2  

Multiplying both sides by 1/√2

( cos x )1/√2 + ( sin x )1/√2= ± 122√

( cos x )( cos π/4 ) + ( sin x )( sin π/4 ) = ± 1/2√2

cos ( x - π/4 ) = ± 1/2√2

Answer 2

Step-by-step explanation:

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